Probability Calculator | Real-Time Statistical Analysis Tool

Advanced Probability Calculations

Probability Distributions

Dice & Coin Simulations

Combinations & Permutations

Real-Time Calculations

Basic Probability Calculator

Favorable Outcomes

Total Possible Outcomes

Probability: 0.5 (50%)

Multiple Event Probability

Event Type

Probability of Event A

(0-1)

Probability of Event B

(0-1)

Combined Probability: 0.25 (25%)

Binomial Distribution

Number of Trials (n)

Success Probability (p)

(0-1)

Number of Successes (k)

Probability

0.2461

Cumulative (≤k)

0.6230

Mean

Normal Distribution

Mean (μ)

Standard Deviation (σ)

X Value

PDF

0.3989

CDF (≤x)

0.5000

Z-Score

0.0000

Combinations & Permutations

Calculation Type

n (Total Items)

r (Selection Size)

Result: 120

Conditional Probability

P(A|B) = P(A∩B) / P(B)

P(A∩B)

(0-1)

P(B)

(0-1)

P(A|B): 0.4 (40%)

Expected Value

Enter values and probabilities (comma separated)

Values

Probabilities

Expected Value: 17

Calculation History

Basic Probability

3/6 = 0.5 (50%)

Combination

10C3 = 120

How to Use the Probability Calculator: A Comprehensive Guide

Understanding Probability Calculations

Probability is a fundamental concept in statistics that measures the likelihood of an event occurring. Our Probability Calculator provides multiple tools to help you calculate various probability scenarios with precision and ease.

Basic Probability Calculator

This tool calculates the simple probability of an event occurring. Enter the number of favorable outcomes and the total number of possible outcomes. The calculator instantly computes the probability as a decimal and percentage.

Multiple Event Probability

Calculate probabilities for multiple events with different relationships:

Independent Events: Events that don't affect each other (e.g., flipping a coin twice)
Dependent Events: The outcome of one event affects the other (e.g., drawing cards without replacement)
Mutually Exclusive Events: Events that cannot occur simultaneously (e.g., rolling a 1 or 6 on a die)

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent trials. Enter the number of trials, probability of success, and number of successes to calculate the probability, cumulative probability, and mean.

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about the mean. Enter the mean, standard deviation, and x-value to calculate the probability density function (PDF), cumulative distribution function (CDF), and z-score.

Combinations and Permutations

Calculate the number of ways to choose or arrange items:

Combinations (nCr): Order doesn't matter (e.g., choosing committee members)
Permutations (nPr): Order matters (e.g., arranging books on a shelf)

Conditional Probability

Calculate the probability of event A occurring given that event B has occurred. Enter the probability of both events occurring (P(A∩B)) and the probability of event B (P(B)).

Expected Value

The expected value represents the average outcome if an experiment is repeated many times. Enter values and their corresponding probabilities as comma-separated lists to calculate the expected value.

Tips for Accurate Calculations

Ensure probabilities are between 0 and 1
For combinations and permutations, r should not exceed n
Standard deviation must be positive for normal distribution
Use the calculation history to track your work

This probability calculator is designed for students, researchers, and professionals who need quick, accurate probability calculations for statistical analysis, research projects, or educational purposes.